OFFSET
1,13
COMMENTS
a(n) counts subsequences of digits of n which denote primes.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(A094535(n)) = n and a(m) < n for m < A094535(n); A039995(39467139) = 100, cf. A205956. - Reinhard Zumkeller, Feb 01 2012
EXAMPLE
a(103) = 3; the 3 primes are 3, 13 and 103.
MATHEMATICA
cnt[n_] := Module[{d = IntegerDigits[n]}, Length[Union[Select[FromDigits /@ Subsets[d], PrimeQ]]]]; Table[cnt[n], {n, 105}] (* T. D. Noe, Jan 31 2012 *)
PROG
(Haskell)
import Data.List (subsequences, nub)
a039995 n = sum $
map a010051 $ nub $ map read (tail $ subsequences $ show n)
-- Reinhard Zumkeller, Jan 31 2012
(Python)
from sympy import isprime
from itertools import chain, combinations as combs
def powerset(s): # nonempty subsets of s
return chain.from_iterable(combs(s, r) for r in range(1, len(s)+1))
def a(n):
ss = set(int("".join(s)) for s in powerset(str(n)))
return sum(1 for k in ss if isprime(k))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Aug 07 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
STATUS
approved